A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications

Nao Hamamuki () and Qing Liu ()
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Nao Hamamuki: Hokkaido University
Qing Liu: Fukuoka University

Partial Differential Equations and Applications, 2021, vol. 2, issue 2, 1-27

Abstract: Abstract This paper is devoted to a game-theoretic approach to the level-set curvature flow equation with nonlinear dynamic boundary conditions. Under the comparison principle for the dynamic boundary problem, we construct a family of deterministic discrete games, whose value functions approximate the unique viscosity solution. We also apply the game approximation to study the convexity preserving properties and the fattening phenomenon for this geometric dynamic boundary problem.

Keywords: Mean curvature flow; Dynamic boundary problems; Discrete games; Viscosity solutions; 35D40; 35K61; 35K93; 49N90 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s42985-021-00076-w

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